Higher-Order Finite Element Methods
Seiten
2003
Chapman & Hall/CRC (Verlag)
978-1-58488-438-5 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-58488-438-5 (ISBN)
Presents a survey of intrinsic techniques and practical implementation of higher-order finite element schemes. This book addresses automatic hp-adaptivity in one and two spatial dimensions. It includes a discussion of suitable data structures and efficient linear solvers. It is suitable for both applied mathematicians and engineers.
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales.
Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity.
Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales.
Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity.
Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.
Pavel Solin, Karel Segeth, Ivo Dolezel
Introduction. Hierarchic Master Elements of Arbitrary Order. Higher-Order Finite Element Discretization. Higher-Order Numerical Quadrature. Numerical Solution of Finite Element Equations. Mesh Optimization, Reference Solutions, and hp-Adaptivity.
| Erscheint lt. Verlag | 28.7.2003 |
|---|---|
| Reihe/Serie | Studies in Advanced Mathematics |
| Zusatzinfo | 78 Tables, black and white; 202 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 725 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-58488-438-X / 158488438X |
| ISBN-13 | 978-1-58488-438-5 / 9781584884385 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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